${\cal N}=8$ supersymmetric mechanics with spin variables from indecomposable multiplets

TL;DR

This paper introduces two new indecomposable ${ m N}=8$, $d=1$ supersymmetric multiplets with spin variables, providing superfield constraints and actions, and demonstrating their on-shell equivalence despite off-shell differences.

Contribution

The paper constructs two novel indecomposable ${ m N}=8$, $d=1$ multiplets with nonlinear scalar superfields and analyzes their supersymmetric models, revealing on-shell equivalence.

Findings

Two new indecomposable ${ m N}=8$, $d=1$ multiplets are defined.

Superfield constraints and invariant actions are explicitly constructed.

The models are shown to be on-shell equivalent despite off-shell differences.

Abstract

We define two new indecomposable (not fully reducible) ${\cal N}=8$, $d=1$ off-shell multiplets and consider the corresponding models of ${\cal N}=8$ supersymmetric mechanics with spin variables. Each multiplet is described off shell by a scalar superfield which is a nonlinear deformation of the standard scalar superfield $X$ carrying the $d=1$ multiplet ${\bf (1,8,7)}$. Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet ${\bf (8,8,0)}$. For both systems we present the manifestly ${\cal N}=8$ supersymmetric superfield constraints, as well as the component off- and on-shell invariant actions, which for one version exactly match those given in arXiv:2402.00539 [hep-th]. The two models differ off shell, but prove to be equivalent to each other on shell, with the spin variables sitting in the adjoint representation of the maximal $R$-symmetry group ${\rm SO}(8)$.